Near-Minimax-Optimal Risk-Sensitive Reinforcement Learning with CVaR
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In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance τ. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Ω(√(τ^-1AK)), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Ω(√(τ^-1SAK)) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of O(√(τ^-1SAK)) under a continuity assumption and in general attains a near-optimal regret of O(τ^-1√(SAK)), which is minimax-optimal for constant τ. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.
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